Add or subtract as indicated. Write answers in lowest terms as needed. $3 and one eighth plus 2 and one fourth$

검증된 단계별 안내

First, convert the mixed numbers to improper fractions. For 3(1/8), multiply the whole number 3 by the denominator 8 and add the numerator 1: $3 \times 8 + 1 = 25$, so $3(1/8) = \frac{25}{8}$. For 2(1/4), multiply 2 by 4 and add 1: $2 \times 4 + 1 = 9$, so $2(1/4) = \frac{9}{4}$.

Next, find a common denominator for the fractions $\frac{25}{8}$ and $\frac{9}{4}$. The denominators are 8 and 4, and the least common denominator (LCD) is 8.

Rewrite $\frac{9}{4}$ with the denominator 8 by multiplying both numerator and denominator by 2: $\frac{9 \times 2}{4 \times 2} = \frac{18}{8}$.

Now, add the two fractions with the common denominator: $\frac{25}{8} + \frac{18}{8} = \frac{25 + 18}{8} = \frac{43}{8}$.

Finally, convert the improper fraction $\frac{43}{8}$ back to a mixed number by dividing 43 by 8. The quotient is the whole number part, and the remainder over 8 is the fractional part.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Mixed Numbers

Mixed numbers combine a whole number and a fraction, such as 3(1/8). To perform operations, they are often converted to improper fractions by multiplying the whole number by the denominator and adding the numerator.

Adding Fractions

To add fractions, they must have a common denominator. If denominators differ, find the least common denominator (LCD), convert each fraction, then add the numerators while keeping the denominator the same.

Simplifying Fractions

After performing addition or subtraction, simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD) to write the answer in lowest terms.

Add or subtract as indicated. Write answers in lowest terms as needed. 318+2143\(\frac{1}{8}\) + 2\(\frac{1}{4}\)